The Argentine struck in injury time to leave the hosts heartbroken after they had twice been denied by the woodwork during a dominant performance.
In truth, a draw would have been a solid result for the Partenopei, with the hosts having twice struck the woodwork through Cesare Bovo and Riccardo Meggiorini and then seen a gilt-edged opportunity go begging when Ciro Immobile fired over while totally unmarked in the area.
However, they stole all three points right at the death when Higuain finished with aplomb after being released by Marek Hamsik.
Giampiero Ventura sprung a couple of surprises with his team selection, as the Torino boss opted to leave star men Alessio Cerci and Immobile on the bench, preferring instead to start with Meggiorini and Paulo Vitor Barreto up front.
Rafael Benitez, meanwhile, elected to recall Dries Mertens at the expense of Lorenzo Insigne, while Federico Fernandez, Gokhan Inler and Jorginho also returned after being left on the bench for the 1-0 Europa League loss to Porto.
Despite the changes, Napoli started sluggishly, and it was Torino which had the first chance of the game 19 minutes in, Meggiorini doing well to control an Omar El Kaddouri pass with his head before unleashing a right-footed volley that drew a smart stop from Pepe Reina.
The Partenopei had an even luckier escape just before the half-hour when Bovo struck the woodwork with a thumping 30-meter drive.
Napoli responded with a couple of long-range strikes from Hamsik and Inler, but there was no disguising the fact that the visitors had struggled dismally to impose themselves on a first half that finished without them having managed a single shot on target.
Napoli finally showed some signs of life moments later when Higuain tested Daniele Padelli for the first time with a low strike that the goalkeeper got down well to deal with.
However, Torino should have been in front in the 53rd minute, but it was again denied by the woodwork, with Meggiorini striking the base of the left post after being slipped in on goal by Barreto.
Reina then pulled off a spectacular save from Matteo Darmian's shot from the edge of the area as Torino ramped up the pressure on the Partenopei.
Higuain was presented with a decent chance to open the scoring when Mertens was felled right on the edge of the area, but the Argentine lost his footing just as he was taking the resulting free kick and the ball flew wide.
By this stage, Torino had sent on top scorer Immobile. He should have broken the deadlock with just 17 minutes remaining, but he fired horribly over the bar after being teed up by Jasmin Kurtic, who had stripped Valon Behrami of possession.
Benitez threw on Insigne for the closing stages and his introduction undoubtedly lifted Napoli, with Mertens going close with just over a minute of normal time remaining. The Belgian was denied by a brilliant save from Padelli, but there was to no stopping Higuain, who produced a fine finish to win the game after latching onto a Hamsik pass.